
where \(\beta \in [0, 1]\)  is a weight parameter and \(\mathcal {L}^{\mbox{\tiny {SAR}}}\)  is the negative thresholded source-to-artifact ratio (SAR) which is a regularization factor to reduce artifacts in the output signal based on the SAR [1]}. \(\mathbf {e}_{\mbox{\tiny {artif}}}\)  is the artifacts in the output signal which can be obtained by decomposing the residual noise \(\mathbf {y}_{:, 1} - \mathbf {s} = \mathbf {e}_{\mbox{\tiny {interf}}} + \mathbf {e}_{\mbox{\tiny {artif}}}\)  where \(\mathbf {e}_{\mbox{\tiny {interf}}}\)  is the orthogonal projection of the residual noise onto the subspace spanned by both \(\mathbf {s}\)  and \(\mathbf {n}\)  [1]}.
